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A309183 (1/4) times the number of n-member subsets of [4n] whose elements sum to a multiple of n.

%I A309183 #11 Jul 18 2019 10:14:03
%S A309183 1,3,19,115,776,5601,42288,328755,2615104,21191128,174303163,
%T A309183 1451430673,12211799224,103655906784,886568153744,7633233556275,
%U A309183 66105170315084,575445689884848,5032380942945322,44191451788247640,389514699013012242,3444925385161998521
%N A309183 (1/4) times the number of n-member subsets of [4n] whose elements sum to a multiple of n.
%C A309183 Also (1/3) times the number of n-member subsets of [4n-1] whose elements sum to a multiple of n.
%H A309183 Alois P. Heinz, <a href="/A309183/b309183.txt">Table of n, a(n) for n = 1..1000</a>
%F A309183 a(n) = 1/(4n) * Sum_{d|n} binomial(4d,d)*(-1)^(n+d)*phi(n/d).
%p A309183 with(numtheory):
%p A309183 a:= n-> add(binomial(4*d, d)*(-1)^(n+d)*
%p A309183         phi(n/d), d in divisors(n))/(4*n):
%p A309183 seq(a(n), n=1..25);
%Y A309183 Column k=4 of A309148.
%K A309183 nonn
%O A309183 1,2
%A A309183 _Alois P. Heinz_, Jul 15 2019